Two Glasses of Water

Jan 21, 2017

RAY: This puzzler was sent in by Frank Juskolka. Frank writes: You have a four-ounce glass and a nine-ounce glass. You have an endless supply of water. You can fill or dump either glass.

TOM: Do you have a plastic bag in your pocket? No. Okay. Just checking.

RAY: It turns out, you can measure six ounces of water using these two glasses. The question is:

1. How many steps are involved; and

B. What's the smallest number of steps in which you can measure six ounces?


RAY: Start with both glasses empty. Step one, you fill the nine-ounce glass. Step two, you pour four ounces from the nine-ounce glass into the four-ounce glass because that's all you can do. Step three, you dump out the four-ounce glass. Now you’ve got five ounces left in the big glass.

Step four, again you fill the four-ounce glass from the nine ounce glass. And step five, again dump the four-ounce glass. So now the four-ounce glass is empty, and you’ve got one ounce in the nine-ounce glass.

Step six, pour the one ounce of water from the nine-ounce glass into the four-ounce glass. Step seven, fill the nine-ounce glass.

TOM: OK. So at the moment here you've got a full nine-ounce glass, and you have one ounce in the four ounce glass.

RAY: So now you pour just enough water from the nine ounce glass to fill the four ounce glass. Which means you're pouring how much out of the nine-ounce glass?

TOM: Three ounces.

RAY: Right, and that leaves how many ounces in the nine ounce glass?

TOM: Six! And we have a winner. The winner is Kim Fern from Honolulu, Hawaii. Congratulations!

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